The length of a vegetable garden is 8 feet longer than three times the width. If the perimeter of the garden is 140 feet, what are the dimensions of the garden?
The length of a vegetable garden is 8 feet longer than three times the width. If the perimeter of the garden is 140 feet, what are the dimensions of the garden?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Problem Statement:
The length of a vegetable garden is 8 feet longer than three times the width. If the perimeter of the garden is 140 feet, what are the dimensions of the garden?
This problem involves finding the dimensions (length and width) of a rectangular vegetable garden given a relationship between the length and width and the total perimeter.
### Let's break this problem down:
1. **Understand the relationship**:
- Let \(W\) be the width of the garden.
- Then, the length \(L\) can be expressed in terms of the width:
\[
L = 3W + 8
\]
2. **Use the perimeter formula**:
- The perimeter \(P\) of a rectangle is given by:
\[
P = 2L + 2W
\]
- Plugging in the given perimeter (140 feet):
\[
140 = 2L + 2W
\]
3. **Substitute the expression for \(L\)**:
- Replace \(L\) with \((3W + 8)\) in the perimeter formula:
\[
140 = 2(3W + 8) + 2W
\]
- Simplify the equation:
\[
140 = 6W + 16 + 2W
\]
\[
140 = 8W + 16
\]
- Solve for \(W\):
\[
140 - 16 = 8W
\]
\[
124 = 8W
\]
\[
W = \frac{124}{8}
\]
\[
W = 15.5
\]
4. **Find the length \(L\)**:
- Using the relationship \(L = 3W + 8\):
\[
L = 3(15.5) + 8
\]
\[
L = 46.5 + 8
\]
\[
L = 54.5
\]
### Solution:
- The dimensions of the vegetable garden are:
- Width (\(W\)): **15.5 feet**
- Length (\(L\)): **54.5 feet**
This solution demonstrates](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fe4f99-9e69-4bef-afe6-80d54e8903ee%2F662c03b8-7a7c-466b-9d9b-b3ec3604fa1e%2F4x2qve_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
The length of a vegetable garden is 8 feet longer than three times the width. If the perimeter of the garden is 140 feet, what are the dimensions of the garden?
This problem involves finding the dimensions (length and width) of a rectangular vegetable garden given a relationship between the length and width and the total perimeter.
### Let's break this problem down:
1. **Understand the relationship**:
- Let \(W\) be the width of the garden.
- Then, the length \(L\) can be expressed in terms of the width:
\[
L = 3W + 8
\]
2. **Use the perimeter formula**:
- The perimeter \(P\) of a rectangle is given by:
\[
P = 2L + 2W
\]
- Plugging in the given perimeter (140 feet):
\[
140 = 2L + 2W
\]
3. **Substitute the expression for \(L\)**:
- Replace \(L\) with \((3W + 8)\) in the perimeter formula:
\[
140 = 2(3W + 8) + 2W
\]
- Simplify the equation:
\[
140 = 6W + 16 + 2W
\]
\[
140 = 8W + 16
\]
- Solve for \(W\):
\[
140 - 16 = 8W
\]
\[
124 = 8W
\]
\[
W = \frac{124}{8}
\]
\[
W = 15.5
\]
4. **Find the length \(L\)**:
- Using the relationship \(L = 3W + 8\):
\[
L = 3(15.5) + 8
\]
\[
L = 46.5 + 8
\]
\[
L = 54.5
\]
### Solution:
- The dimensions of the vegetable garden are:
- Width (\(W\)): **15.5 feet**
- Length (\(L\)): **54.5 feet**
This solution demonstrates
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